MAE 185 Numerical Analysis in Mechanical Engineering SPRING 2006, UCI. Mechanical Engineering dept.


Personal course web site by Nasser M. Abbasi, last updated 062206



Introduction and contact information. 1


Lecture notes. 3

Homeworks. 4

Discussion notes. 4

Download section. 4

Useful Links. 5

Free compilers. 5

Fortran resources. 5

Fortran official language reference manuals. 5

Fortran tutorials and help pages and other useful links. 5

Fortran 90/95 Tutorials and references. 6

Links specific to floating point Arithmeti and Numerical computation. 7



Introduction and contact information

This course was in spring 2006 by Professor Donald Dabdub from Mechanical eng. Dept, UCI.

I was the TA for the course, and will use this web file to keep track of information ref. this course and my notes, etc…



Professor Dabdub  web site http://albeniz.eng.uci.edu/dabdub/  

Email: ddabdub@uci.edu

Phone: 949-824-6126, EG 4226

Office Hours  Tuesday and Thursday  2-3 PM  


Official class web site  http://albeniz.eng.uci.edu/mae185


TA: Nasser M. Abbasi

Email: nabbasi@uci.edu

Office hours: Monday, Wednesday 1:00-2:00 PM

Office: Located inside Professor Dabdub lab. in EG 3102


Class info from the schedule




Text book






Table of Contents



Systems of Linear Algebraic Equations.

Nonlinear Algebraic Equations.


Statistics and Least-Squares Approximation.

Curve Fitting.


Differentiation and Integration.

Ordinary Differential Equations.


Matrix Eigenproblems.

Introduction to Partial Differential Equations.

Design and Optimization.




Answers to Selected Problems.






Final exam problem [PDF]

Additional instructions [HTML]


Note on recording CPU time:

You only need to record the CPU time at the end of each method, which will result in recording CPU time 3 times only at t=30, once per method. See this for a Fortran Template  [HTML]


my solution to final exam [HTML]

Fortran guide note for class HTML

Lecture notes

These are my own notes I wrote down during the class lectures.


  1. Tuesday_April_4_2006   [PDF]
  2. Thursday_April_6_2004  [PDF]
  3. Tuesday_April_11_2006   [PDF]
    This is my solution for quiz professor gave about outputting the big and the small number without use of IF nor DO loops.
  4. Thursday April 14, 2006. Lecture was a FORTRAN exam.  
    Here are my solutions
  5. Tuesday_April_18_2006
  6. Thursday April 20, 2006
  7. Tuesday_April_25_2006
  8. Thursday April 27 2006.
  9. Tuesday_May_2_2006.pdf
  10. Thursday_May_4_2006.pdf
  11. Tuesday_May_9_2006.pdf   
  12. Thursday_May_11_2004.pdf
  13. Tuesday May16 2006. TODO
  14. Thursday May 18, 2006. Midterm.
    Questions: midterm_exam_MAE_185_s06.pdf
    Answers: PDF format  midterm_solutions.pdf
                    HTML format midterm_solutions.htm
     Take home part of the midrerm solution  [HTML]
  15. Tuesday May 23 2006.  Lecture was on Romberg Integration and review of Trapezoidal and simpson’s integration method.
  16. Thursday May 25, 2006. Lecture was on Gaussian  quadrature. And the following iterative methods for solving Ax=b: Jacboi, Gauss-seidel, and SOR.
    My scratch notes [PDF,   HTML]
    The following is a note on Gaussian  quadrature  with worked examples. [PDF, HTML]
  17. Tuesday May 30,2006 [PDF]
  18. Thursday June 1, 2006  [PDF]
  19. Tuesday June 6, 2006 [PDF]




  1. HW1 [PDF]
  2. HW2 problem. Assigned on April 27, 2006 [image]
  3. HW3. Assigned on Tuesday May 9,2006. Generate and plot the Julian sets for
  4. HW4. On Romberg integration. [HTML]



Discussion notes

  1. Friday_april_7_2006
  2. Friday April 14 2006. Went over FORTRAN exam solution.
  3. Friday April 21. Solution of Ax=b, and example using Gaussian elimination method. These are informal discussion notes.
    This is a diagram that summarizes the methods. HTML  PDF  PNG
  4. Friday April 28 2006.
  5. friday_may_5_2006.pdf
  6. notes for Friday May 12, 2006 are here in PDF format. Here in HTML format.
  7. Friday May 19, 2006.
  8. Friday May 26, 2006. Posted notes on Gaussian Quadrature. [PDF, HTML]
  9. Friday June 2. Review of PDE’s classification, numerical solution of PDE using centered difference, classification of B.C’s, and review of using Numman stability criteria.




Download section

I’ll put here things for downloading. As needed.


  1. This PDF file contains list of FORTRAN77 intrinsic function from the back of the book by Etter. Added April 24,2006
  2. This PDF file contains list of FORTRAN77 intrinsic function from the back of the book by Ellis. Added April 24,2006
  3. This PDF file is Intel FORTRAN 90 Language reference manual.
  4. This PDF file is Intel FORTRAN 90 Library reference manual.
  5. FORTRAN 77 Manual (X3J3) HTML version
  6. Historical FORTRAN manual. This is the 1956 FORTRAN manual in PDF written for the IBM704. This is I think is FORTRAN II. Classic.
  7. Free book on FORTRAN 77 in PDF format, by Clive G. Page.
  8. Free book on FORTRAN 77 by Ian Chivers  and Jane S. in PDF format.

9.      These are the WATCOM free FORTRAN manuals. They can be downloaded from http://www.openwatcom.org/index.php/Manuals .



Useful Links

Free compilers

  1. http://www.openwatcom.org/index.php/Download   This is free WATCOM F77 compiler for windows.
  2. http://www.silverfrost.com/32/ftn95/ftn95_personal_edition.asp   This is a FREE FORTRAN 95 compiler for windows.  Salford F95. I tried it and it is nice, it has a GUI front end, and even a debugger one can step through.
  3. http://www.cygwin.com/  Cygwin is a complete unix environment for windows. Download and install. Make sure to select all the tools to obtain the GNU fortran compilers as well.
  4. http://www.gnu.org/software/fortran/fortran.html   GNU fortran 77 web site.
  5. http://www.g95.org/  free g95 compiler group.
  6. http://www.gfortran.org/   another free fortran compiler site.



Fortran resources

Fortran official language reference manuals


  1. Fortran 95 language manual.
     http://j3-fortran.org/doc/year/97/97-007r2/pdf/97-007r2.pdf  here is local copy in the case the above goes away.
  2. http://www.openwatcom.org/index.php/Manuals   FORTRAN 77 manuals.
  3. http://gcc.gnu.org/onlinedocs/gfortran/index.html  GNU FORTRAN 95 on-line manual.
  4. http://j3-fortran.org/doc/standing/007/  This web site contain FORTRAN 2003 early drafts and language specifications for free download.


Fortran tutorials and help pages and other useful links

  1. http://fortran.domeintje.net/   “Fortran start page”. According to author. This web page has lots of good links to Fortran resources.  Such as FAQ’s and compilers and other Fortran links.
  2. http://library.lanl.gov/numerical/bookf90pdf.html  The complete Numerical reciepies book in Fortran90 on-line. This is the parent page http://library.lanl.gov/numerical/  which includes F77 Numerical recipes.
  3. http://www.cs.mtu.edu/~shene/COURSES/cs201/NOTES/fortran.html  A FORTRAN tutorial. good basic notes on FORTRAN by Dr. C.-K. Shene
  4. http://www.star.le.ac.uk/~cgp/f90course/f90.html  Good notes that makes it easy to move to FORTRAN 90 from FORTRAN 77
  5. http://www.nsc.liu.se/~boein/f77to90/   FORTRAN90 for FORTRAN77 programmers. An on-line tutorial.
  6. http://www.dmoz.org/Computers/Programming/Languages/Fortran/   FORTRAN page on the open directory languages web site.
  7. http://www.j3-fortran.org/  The FORTRAN standards committee. In this site one can download free copies of FORTRAN 2003 standard.
  8. http://www.csit.fsu.edu/~burkardt/f_src/f_src.html   John Burkardt collection of F90 routines.
  9. http://www.fortranlib.com/  The fortran library site
  10. http://www.fortran.com/  The FORTRAN company
  11. http://gershwin.ens.fr/vdaniel/Doc-Locale/Langages-Program-Scientific/Fortran/Tutorial/index.htm  a fortran tutorial on F77.
  12. http://www.ibiblio.org/pub/languages/fortran/unfp.html  Some notes on fortran.
  13. http://www.star.le.ac.uk/~cgp/prof77.html  Some one Guide for F77. I went over this, look good.
  14. http://www.netlib.org/  free fortran software to download
  15. http://www.engineering.usu.edu/cee/faculty/gurro/Software_Calculators/Fortran_g77/MyFortranG77Page.html   an F77 web page.
  16. http://www.obliquity.com/computer/fortran/function.html  List of all F77 intrinsic functions.
  17. http://www.obliquity.com/computer/fortran/  F77 reference web page
  18. http://www.ictp.trieste.it/~manuals/programming/sun/fortran/   Sun F77 page




Fortran 90/95 Tutorials and references


(These below I found in Intel manual, I copied here)





Links specific to floating point Arithmeti and Numerical computation


  1. http://docs.sun.com/source/806-3568/ncg_goldberg.html  This is a good document by David Goldberg.  Good reading.
  2. http://www.nr.com/  Numerical recipes.